Methods and apparatus to incorporate saturation effects into marketing mix models

ABSTRACT

Methods and apparatus to incorporate saturation effects into marketing mix models are disclosed. An example apparatus includes means for converting adstock data associated with an advertising campaign into effective reached realized (ERR) data based on a first saturation curve, the adstock data corresponding to adstocked gross rating points generated from marketing mix input data. The apparatus further including means for performing regression analysis to: identify the first saturation curve from among a plurality of plausible curves based on a fit of different ones of the plurality of plausible curves to the marketing mix input data, the first saturation curve to define a relationship indicative of saturation effects of the advertising campaign on a target audience of the advertising campaign; and determine an impact of the advertising campaign on sales during a period of interest based on a regression analysis of the ERR data relative to sales data.

RELATED APPLICATIONS

This patent arises from a continuation of U.S. patent application Ser.No. 16/934,682, now U.S. Pat. No. 11,361,342, which was filed on Jul.21, 2020. U.S. patent application Ser. No. 16/934,682 is a continuationof U.S. patent application Ser. No. 15/659,313, now U.S. Pat. No.10,755,299, which was filed on Jul. 25, 2017. U.S. patent applicationSer. No. 15/659,313 is a divisional of U.S. patent application Ser. No.13/835,695, now U.S. Pat. No. 9,721,271, which was filed on Mar. 15,2013. U.S. patent application Ser. No. 16/934,682, U.S. patentapplication Ser. No. 15/659,313, and U.S. patent application Ser. No.13/835,695 are hereby incorporated herein by reference in theirrespective entireties. Priority to U.S. patent application Ser. No.16/934,682, U.S. patent application Ser. No. 15/659,313, and U.S. patentapplication Ser. No. 13/835,695 is hereby claimed.

FIELD OF THE DISCLOSURE

This disclosure relates generally to marketing mix models and, moreparticularly, to methods and apparatus to incorporate saturation effectsinto marketing mix models.

BACKGROUND

Marketing mix modeling is an analytical tool used in market researchthat is based on the statistical analysis, such as multivariateregression, of historical sales and marketing data to estimate theimpact or contribution of various advertising campaigns via differentmedia on the sales of corresponding advertised products or services.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a graph represented raw GRPs and correspondingAdstocked GRPs delivered over a ten week period for an exampleadvertising campaign.

FIG. 2 illustrates a graph with a response curve fit to data pointsoutput from a known marketing mix model.

FIGS. 3 and 4 illustrate graphs containing example saturation curves.

FIGS. 5-7 illustrate example tables for Volume, Scale, and Shapeparameters that define saturation equations corresponding to the examplesaturation curves of FIGS. 3 and 4

FIGS. 8-11 illustrate graphs that represent the Effective Reach Realizedfrom the Adstocked GRPs of FIG. 1 based on the saturation curves ofFIGS. 3 and 4 .

FIG. 12 illustrates an example response curve fit to the data points ofFIG. 2 calculated in accordance with the teachings disclosed herein.

FIG. 13 illustrates a response curve fit to data points associated withlift for a particular advertising campaign output from a known marketingmix model (e.g., without saturation) and an example response curve fitto data points associated with lift for the same advertising campaignoutput from a marketing mix model generated in accordance with theteachings disclosed herein (e.g., with saturation).

FIG. 14 is a schematic illustration of an example marketing mix modelgenerator constructed in accordance with the teachings disclosed herein.

FIG. 15 is a flowcharts representative of example machine readableinstructions for implementing the example marketing mix model generatorof FIG. 14 to generate a marketing mix model.

FIG. 16 is a flowcharts representative of example machine readableinstructions for implementing the example marketing mix model generatorof FIG. 14 to calculate plausible saturation curves to generate themarketing mix model as in FIG. 15 .

FIG. 17 is a flowcharts representative of example machine readableinstructions for implementing the example marketing mix model generatorof FIG. 14 to simulate an advertising campaign to calculate plausiblesaturation curves as in FIG. 16 .

FIG. 18 is a schematic diagram of an example processor platform capableof executing the instructions of FIGS. 15-17 to implement the examplemarketing mix model generator of FIG. 14 .

DETAILED DESCRIPTION

Market analysts may be chartered with one or more tasks related tounderstanding how different factors impact sales over time. The marketanalysts may exert such efforts in response to client requests, in whichclients may include manufacturers, retailers, merchants and/orwholesalers that wish to appreciate and/or otherwise understand factorsthat help and/or hurt sales. Factors capable of affecting sales include,but are not limited to promotional activity (e.g., televisionpromotions, radio promotions, newsprint promotions, online promotions,etc.), macro-economic factors and seasonality.

To better understand what relationships exist between one or morefactors, a statistical regression analysis may be performed usingindependent and dependent variables related to the client salesenvironment. Independent variables may include a variety of factors,some of which are under the control of the client such as, for example,advertising campaign media types (e.g., television, radio, etc.),campaign target demographics, campaign dates and/or time-of-day,geographic locations of the advertising campaigns, etc. The regressionanalysis provides market analysts with one or more coefficientsindicative of a manner in which independent variable affect dependentvariables. In other words, the one or more coefficient weights indicatea measure of contribution or impact of a particular advertising campaignor other promotional activities on sales (e.g., an amount of lift insales due to the particular marketing endeavor). Based on the determinedcontribution of each advertising campaign on sales included in amarketing mix model estimation, future sales may be predicted and/or thearrangement of a mixed marketing campaign may be enhanced (e.g.,optimized) within constraints defined by an allotted marketing budget.

In many known marketing mix systems, inputs for promotional activitiesand/or advertising campaigns are based on gross rating points (GRPs),which are a measure of an amount of advertising effort over a specifiedperiod. More particularly, GRPs is a term of art, which as used herein,refers to a measure of an amount of advertising exposures produced by aspecific advertising campaign during a specific period of time (or thesum of all exposures from multiple campaigns during a period of time).GRPs are calculated by multiplying the percentage of a target audiencereached by (e.g., exposed to) an advertisement of the campaign with thefrequency of exposure (e.g., the number of times the audience is exposedto the advertisement) during a set period of time (e.g., in a one weekperiod). For example, if a television advertisement is aired once duringa week and reaches 75% of a target audience, the resulting GRP valuewould be 75 (75%×1). Similarly, if the television advertisement is airedthree times with a reach of 75% each time, the resulting GRP value wouldbe 225 (75%×3). The amount of GRPs delivered for an advertising campaigncan be correlated with the level of spending on advertisements. That is,an increase in expenditures on a campaign corresponds to an increase inGRPs because increased spending typically implies having more instancesof an advertisement and/or reaching out to more of the target audience.

Generating or estimating a marketing mix model is based on historicalsales and marketing data (e.g., GRPs for each advertising campaign to beanalyzed) over an extended period of interest (e.g., 2 months, 12months, 2 years, etc.). In many known model estimation systems the GRPspurchased or delivered during the period of interest for each campaignare broken down by a consistent incremental time period (e.g., each weekduring the campaign). Using such data, time-phased GRPs can be visuallyrepresented via a graph as shown in FIG. 1 . In particular, FIG. 1illustrates an example graph 100 with bars 102 representing GRPs(Y-axis) purchased over a ten week period of time (X-axis) (each of theweeks during the diagramed period of interest is identified bycorresponding reference numerals 104, 106, 108, 110, 112, 114, 116, 118,120, 122).

In many advertising campaigns, GRPs delivered over an extended period ofinterest will have weeks where the GRP value is 0 because no advertisingfor the particular campaign occurred during the corresponding weeks. Forexample, the GRPs associated with a limited run advertising campaignwill be zero during the period of interest before and after thecampaign. In other examples, GRPs will be zero between periods ofactivity in a campaign scheduled on an episodic, periodic, or seasonalbasis. Thus, as shown by the GRPs associated with the exampleadvertising campaign diagramed in the graph 100 of FIG. 1 , the first,sixth, ninth, and tenth weeks 104, 114, 120, 122 have a GRP value of 0whereas the remaining weeks, 106, 108, 110, 112, 116, 118 indicate thatGRPs were purchased in amounts ranging from 20 GRPs (during the secondweek 106) to 300 GRPs (during the fourth week 110).

Using the GRPs delivered during each segmented time period for eachcampaign to be analyzed in connection with sales data for the entireperiod of interest, a regression model can be built to estimate thecontribution or impact of each campaign on the sales. However, it isknown that time-phased GRPs (e.g., GRPs grouped by week during theperiod of interest) are a poor predictor of sales over time becausepeople do not always respond to an advertisement immediately after beingexposed to the advertisement. To use the graph 100 as an example, withthe large advertising push that occurred during the fourth week 110(e.g., 300 GRPs delivered), it is probable that many people were exposedto the advertisement at least once that week. However, some of thepeople exposed during the fourth week 110 may not follow through with apurchase of the advertised product or service until the sixth week 114diagramed in the graph 100. As such, when determining the contributionof the diagramed advertising campaign on sales relative to other factorsin a regression analysis, the sale made during the sixth week 114 (whenno GRPs were purchased) would incorrectly be attributed to somethingother than the advertising campaign of graph 100 because the sale wasbased on an advertisement from the fourth week 110 (when 300 GRPs weredelivered). In other words, there was a two week lag of time from whensome people were exposed to the advertisement (during the fourth week110) and when they made the purchase (during the sixth week 114).

While there may be a time lag between an advertisement and a response(e.g., a sale) by members of a target audience exposed to theadvertisement, the lag time cannot be accounted for by a mere shift intime. On the contrary, most responses (e.g., sales) due to anadvertisement occur relatively soon after the occurrence of theadvertisement with the advertisement eliciting fewer and fewer responsesas time moves on. In other words, the actual effect of GRPs delivered ata certain point in time may be realized over a span of time, but theeffect decreases as the span of time increases. Many marketing mixsystems account for the decay of the effect realized of GRPs over timethrough adstocking. Adstocking is a marketing research technique thattakes raw GRPs purchased during one period of time and distributes themover a range of future periods. The effective GRPs realized at any pointin time, based on the temporal distribution of the effect of the rawGRPs, is herein referred to as Adstocked GRPs. Adstocked GRPs are basedon an assumption that the effect realized from GRPs delivered at acertain point in time decays exponentially over time. Thus, based on adecay factor (D), the Adstocked GRPs (A) for a time period (t) as afunction of raw GRPs (x_(t)) can be calculated as follows:A(x _(t))=D x _(t)+(1−D)A(x _(t-1))  Equation 1.Accordingly, using a decay factor of D=0.5 to transform the raw GRPs(represented by the bars 102) plotted in the graph 100 of FIG. 1 , theresulting Adstocked GRPs are represented by the dotted line 124. Thus,while 300 GRPs are delivered during the fourth week 110, the effectiveGRPS realized that week is only 170 GRPs (some amount of whichcorrespond to the lag time effect of the GRPs delivered during thesecond and third weeks 106, 108 of the period being analyzed). Theremaining portion of the 300 GRPs purchased during the fourth week 110is realized in incrementally decreasing amounts (due to adstockingdecay) over the subsequent weeks 112, 114, 116, 118, 120, 122 ascombined with subsequent GRPs purchased.

As with the raw GRPs represented by the bars 102, the Adstocked GRPscorrespond to discrete data points associated with the effective GRPsrealized during each corresponding week 104, 106, 108, 110, 112, 114,116, 118 120, 122. However, to highlight the smoothing effect of thetransformation of the raw GRPs to Adstocked GRPs, the data points in thegraph 100 of FIG. 1 are shown connected by the line 124. Havingcalculated the Adstocked GRPs for each advertising campaign to beanalyzed for model estimation, many marketing mix systems then perform alinear regression to generate a marketing mix model that estimates thecontribution of each of the advertising campaigns on sales over theperiod of interest being modeled. Once the contributions of eachadvertising campaign are determined (as well as any other factorsconsidered in the regression), the results of the model can be evaluatedto estimate future sales based on scheduled advertising campaigns goingforward. Furthermore, the results of marketing mix models can beevaluated to make business decisions such as determining marketingexpenditures across media types and/or geographic areas to enhance(e.g., optimize) a return on investment within budgetary constraintsand/or other considerations.

While analyzing Adstocked GRPs provides a better model of the impact ofmarketing on sales than analyzing raw GRPs, marketing mix modelsgenerated based on Adstocked GRPs are subject to several limitations.For instance, it is well known that there are diminishing returnsassociated with increased marketing expenditures (e.g., increased GRPspurchased) due to the target audience becoming saturated. That is, therelationship between the amount of GRPs purchased and the correspondingachieved is not linear. Rather, as a target audience is exposed more andmore to an advertising message (e.g., increasing GRPs), the increase inreach is smaller and smaller because fewer and fewer target audiencemembers will have yet to be exposed to the advertising message. Further,a diminishing impact on reach implies a diminishing effect on salesbecause once the target audience has been reached, they will eitherrespond with a purchase or choose not to respond. Any additionaladvertising will have little impact and merely serves to saturate thetarget audience more. A target audience is said to be saturated when thenumber of GRPs in a given period exceeds a threshold value at whichpoint further marketing expenditures are greater than any anticipatedbenefit to be drawn therefrom.

While the diminishing returns effects of marketing expenditures are wellknown, known marketing mix systems do not account for such effects ingenerating marketing mix models. One reason for not incorporatingsaturation effects in current marketing mix models estimation is thatthe nature of saturation cannot be determined based on the marketing mixmodel input data used to generate the model. As a result, marketing mixmodels implemented today only output a linear relationship between GRPsand resulting lift in sales which cannot be reliably used to forecastfuture sales or plan future marketing endeavors. For example, FIG. 2illustrates a graph 200 with a response curve 202 generated from a knownmarketing mix model. As shown in the graph 200, the response curve 202,based upon a best fit curve of the calculated lift in sales contributedby the corresponding advertising campaign, is a straight line.Accordingly, the response curve 202 cannot be used to forecast futuresales or project the impact of increasing GRPs with any reliability.Some analysts attempt to adjust marketing mix systems results, such asthe response curve 202 of FIG. 2 , to account for saturation after modelestimation is completed. However, this process is prone to error and isnot especially accurate because it is based on the assumptions ofanalysts playing with the numbers to arrive at what the analysts thinkis curve that reasonable accounts for saturation without having anygrounding in hard data associated with the particular advertisingcampaign being analyzed. Furthermore, the process of adjusting amarketing mix model after the fact requires analysts to correct theresponse curve for each campaign being analyzed in each model to beevaluated. As such, the process can be time consuming and requireshuman-based expertise rather than generating response curves that can bereliably used in forecasting sales and/or planning future marketingcampaigns.

The teachings disclosed herein overcome these obstacles by incorporatingthe effects of saturation directly into marketing mix model estimationto produce more accurate results with more realistic response curves forbetter forecasting of sales and/or planning of future marketingendeavors. As disclosed herein, the inclusion of saturation into modelestimation is based on estimating an initial saturation curve based onan initial estimate of a penetration and an effective frequencyassociated with each of the advertising campaigns to be analyzed. Insuch examples, the initial estimate for penetration and effectivefrequency are used to define ranges of plausible penetrations and rangesof plausible effective frequencies to define corresponding ranges ofplausible saturation curves that may be analyzed against the marketingmix model input data to determine the curve that best fits the data. Theinitial estimate for the penetration and effective frequency for eachadvertising campaign can be based on a variety of known attributesand/or characteristics associated with the corresponding campaigns. Forexample, estimates of penetration and effective frequency in someexamples are based on the media type of the campaign, demographicinformation associated with the target audience of the campaign, thegeographic region of the advertising campaign, the type of product (orservice) associated with advertising campaign, the comparablepenetration and/or effective frequency of comparable campaignsassociated with related and/or competing products, the complexity of theadvertising copy (e.g., the advertising message) associated with thecampaign, and/or the results of previous marketing mix studies.Additionally or alternatively, in some examples, best fitting saturationcurves determined for particular advertising campaigns (e.g., based onany of the attributes described above) can be saved in a database foruse as an initial estimate in determining a best fitting saturationcurve for similar advertising campaigns in a later developed marketingmix model. In this manner, an iterative feedback loop can be developedthat uses the calculated best fitting curves from previous modelestimations into calculated best fitting curves for subsequent modelestimation thereby refining the estimation process over time.Furthermore, the methods and apparatus disclosed herein enable thecalculation (or retrieval) of saturation curves for incorporatingsaturation effects into model estimation in an automated way to reduceor eliminate the tuning of response curves generated from models bymarket analysts after the fact.

In some examples, a saturation equation that defines a best fittingsaturation curve associated with each particular advertising campaignbeing analyzed is used to convert the effective GRPs realized (i.e.,Adstocked GRPs) at each segment of time during the period of interestinto a corresponding measure of Effective Reach Realized (ERR) for eachsegment of time. The ERR for a particular advertising campaign is usedherein to refer to the percentage of target audience members effectivelyexposed to an advertisement a sufficient number of times to elicit aresponse (e.g., a sale). ERR is distinguished from effective reach,which is a term of art, in that effective reach is a measure of thepercentage of target audience members actually exposed to anadvertisement during a specified period. In contrast, as used herein,ERR is described in terms of “effective” exposure during a time period,which takes into account the time lag or decaying effect ofadvertisements over time. Thus, an individual exposed to anadvertisement one week may count towards the ERR of the correspondingadvertisement in a subsequent week because of the temporal distributionof GRPs built into the Adstocked GRPs from which ERR is calculated.

Once the ERR for each campaign is calculated during each segmented pointof time the period of interest being analyzed, the resulting data may berun through a regression analysis as is done in known marketing mixsystems. That is, each advertising campaign (and all other factors underconsideration) is analyzed against sales data for the period of interestto determine the lift in sales due to each advertising campaign tothereby generate a marketing mix model for subsequent evaluation topredict and/or plan the effectiveness of future marketing efforts. Byaccounting for saturation via the ERR during model estimation, responsecurves output by the model will be more reliable than the responsecurves generated from known marketing mix models. Another advantage ofaccounting for saturation within the model estimation process via theERR, is that ERR is more closely related to purchase decisions thanAdstocked GRPs. As a result, the marketing mix model generated with theERR data is much more accurate and reliable.

The ERR for an advertising campaign is most accurate if the saturationequation from which the ERR was calculated corresponds to the real-worlddiminishing effects of the advertising campaign as GRPs increase. Insome examples, the saturation equation is assumed to match a reach curve(or saturation curve) associated with the advertising campaign. Asaturation curve is a curve that results from plotting the total reachof an advertising campaign during a specified period against a totalamount of Adstocked GRPs delivered during the period. FIGS. 3 and 4illustrate graphs 300, 400 containing example saturation curves 302,304, 402, 404. In some examples, the saturation equation (e.g., defininga saturation curve) for a given advertising campaign is assumed todepend on three factors: (1) the amount of advertising effort (asmeasured in GRPs), (2) the effective frequency of the campaign, (3) andthe penetration of the campaign. The effective frequency of anadvertising campaign is defined as the average number of times a personmust be exposed to an advertising message before a response is made(e.g., a decision to purchase the advertised product or service). Theeffective frequency depends upon the complexity of an advertisingmessage. For example, a person exposed to a straight forward promotionaladvertisement (e.g., a coupon that offers a discount on a directlyidentified product) probably only needs to see the coupon once to decidewhether or not to respond to the advertisement by purchasing theproduct. In contrast, a more complicated advertising message (e.g., atelevision advertisement spot that only identifies a product or brand atthe very end of the spot) may require multiple exposures (e.g., 2, 3, 5,etc.) by an individual to sufficiently grasp the concept of theadvertisement and formulate an opinion about whether to respond to theadvertisement (e.g., make a purchase). As the actual number of exposuresrequired for a particular individual to respond to an advertisement mayvary from person to person, the effective frequency of an advertisingcampaign is expressed as an average. Further, effective frequency can beexpressed in fractions in addition to whole numbers because of thevariance in how many exposures are sufficient to elicit a response.

The penetration of an advertising campaign corresponds to the maximumnumber of individuals (or households) of a target population that canpossibly be reached via a particular medium. Expressed differently, inone example, penetration is defined as the percentage of individuals (orhouseholds) that are physically able to be exposed to a medium. Forexample, approximately 98% of U.S. households own a television.Therefore, the penetration of a television advertisement could reach98%. However, the penetration for a particular advertising campaign mayvary if it is limited to cable television (subscribed to by a somewhatsmaller percentage of households) or focused on a particular demographic(e.g., television ownership may be lower for males aged 18-24 than it isfor the nation as a whole). In some examples, penetration is derivedfrom the type of media used in the advertising campaign and demographicinformation associated with and the particular demographics of thetarget audience of the advertising campaign. In some such examples, thedemographic information is collected through audience measurementsurveys and/or is obtained from audience measurement entities, such asThe Nielsen Company, that collect such data. Additionally oralternatively, in some examples, other factors and/or attributesassociated with the advertising campaign are considered in determiningthe penetration corresponding to the campaign.

A saturation or reach curve (corresponding to a saturation equation usedin some examples disclosed herein) can be shown graphically by plottingGRPs (e.g., Adstocked GRPs) against reach for a fixed effectivefrequency and fixed penetration. For example, as illustrated in thegraph 300 of FIG. 3 , the saturation curves 302, 304 are associated withthe same penetration but different effective frequencies. In particular,the curve 302 corresponds to an effective frequency of 1 and apenetration of 20%, while the curve 304 corresponds to an effectivefrequency of 4 and a penetration of 20%. For comparison, the graph 400of FIG. 4 , the saturation curves 402, 404 are both associated with apenetration of 95%, with the curve 402 corresponding to an effectivefrequency of 1 and the curve 404 corresponding to an effective frequencyof 4. As illustrated in the graphs 300, 400, as GRPs increase the curves302, 304, 402, 404 level off, indicating the diminishing returns effectdue to saturation. More specifically, the point at which each of thecurves 302, 304, 402, 404 levels off corresponds to the penetrationassociated with the curve. That is, the saturation curves 302, 304asymptotically approach a reach of 20% as GRPs increase and saturationcurves 402, 404 asymptotically approach a reach of 95%. Further, theshape of each curve 302, 304, 402, 404 is based on the effectivefrequency. In particular, for an effective frequency of 1, the resultingcurve (e.g., the curves 302, 402) is a C-shaped curve characterized by aconstantly diminishing slope. For effective frequencies greater than 1,the resulting curves (e.g., the curves 304, 404) are S-shaped;characterized by a slope that initially increases with increasing GRPsand then decreases thereafter. For the S-shaped saturation curves, ahigher effective frequency corresponds to a longer leading tail on theresulting curve.

In some examples, to calculate a saturation equation to be used totransform Adstocked GRPs to ERR, a reach curve (e.g., saturation curve)is generated by plotting data points of known GRPs against known reach,and determining a line that best fits the plotted data points. In someinstances, real-world data of GRPs and corresponding reach may be takenfrom prior marketing research studies and/or previously generatedmarketing mix models that have been shown to fit real-world data. Inother instances, where such data is unavailable, the GRPs andcorresponding reach may be derived from simulations of advertisingcampaigns. For example, a simulated population size of a target audiencemay be defined (e.g., 10,000 individuals) and a subset of the populationis selected based on the known penetration for the campaign (e.g., 8,000individuals based on 80% penetration). As described above, thepenetration in some such examples is inferred from one or morecharacteristics associated with the campaign to be simulated(corresponding to the actual advertising campaign to be analyzed). Suchcharacteristics include the media type of the campaign, demographicinformation associated with the target audience of the campaign, and thegeographic region of the advertising campaign. From the selected subset,a single advertisement is simulated with a defined GRP value. Forexample, assume the advertisement is associated with 10 GRPs. As this isa single advertisement there will be no duplicate exposures such thatthe reach would be 10% of the target population (e.g., 1,000individuals). Accordingly, 1,000 individuals (10% of the total 10,000target population) of the 8,000 subset of the target population arerandomly selected as being exposed to the advertisement. The process isthen repeated with a second simulated advertisement, except that duringthe second simulated advertisement, at least some of the 1,000individuals exposed to the first simulated advertisement will likely berandomly selected for exposure to the second advertisement. Accordingly,this duplicate set of individuals does not add to the total reachobtained by the combined first and second advertisements (correspondingto the combined GRPs associated with both advertisements). Thesimulation continues with the total GRPs simulated with each successiveadvertisement plotted against the total reach obtained by all theadvertisements until the total reach approaches the penetration level.Additionally, this same simulation process is followed to plot the totalreach of individuals exposed to at least two of the simulatedadvertisement and/or any other number to generate a plot defining acurve associated with a corresponding effective frequency.

With simulated data points plotted for a reach curve, a saturationequation can then be defined that corresponds to a line that fits thesimulated data. Reach curves (e.g., saturation curves), such as thecurves 302, 304, 402, 404 shown in FIGS. 3 and 4 , closely match Weibullfunctions with parameters for Volume, Scale, and Shape. Thus, in someexamples, once a simulation has been completed as described above, asaturation equation that defines the ERR (S) for a time period (t) as afunction of Adstocked GRPs (x_(t)), can be expressed as follows:S(x _(t))=Volume(1−e{circumflex over ( )}(−(x _(t)/Scale){circumflexover ( )}Shape)  Equation 2.

In Equation 2, the Volume, Scale, and Shape parameters are adjustedappropriately to define a curve that best fits the simulated data. FIGS.5-7 illustrate example tables 500, 600, 700 for Volume (FIG. 5 ), Scale(FIG. 6 ), and Shape (FIG. 7 ) that define a curve that best fitssimulated data generated based on the effective frequencies andpenetrations corresponding to the saturation curves 302, 304, 402, 404of FIGS. 3 and 4 . That is, the corresponding values provided in thetables 500, 600, 700 entered into equation 2 produce the curves 302,304, 402, 404 shown in FIGS. 3 and 4 . By simulating a campaigncorresponding to any anticipated penetration (e.g., 3%, 6%, 9%, . . . ,99%) paired with any anticipated effective frequency (e.g., 1, 1.5, 2,2.5, . . . , 6) full tables of Volume, Scale, and Shape can be createdand stored to quickly look up the parameters to be entered into equation2 to define any corresponding saturation curve such that the simulationdoes not need to be repeated each time a saturation curve needs to becalculated. Although the example values in the tables 500, 600, 700 ofFIGS. 5-7 correspond to equation 2, in some examples, differentequation(s) are used that define a curve that suitably fits simulateddata and correspondingly different tables may be generated for quickretrieval of the resulting saturation equations.

Where saturation equations calculated for a given penetration andeffective frequency are based on simulated advertising campaigns, thesaturation equations may not exactly model the real-world data beinganalyzed for marketing mix model estimation. Accordingly, in someexamples, the identified penetration for a particular advertisingcampaign (e.g., based on audience measurement data including media typeand demographic information and/or other factors associated with thecampaign) and the identified effective frequency for the campaign (e.g.,based on the nature and complexity of the advertisement and/or otherfactors associated with the campaign) are only initial estimates of thepenetration and effective frequency and the resulting saturation curveis only a first best guess. In some examples, based on the initialestimate for the effective frequency and penetration of an advertisingcampaign, a range of plausible effective frequencies and a range ofplausible penetrations can be determined to calculate (or look up) arange of plausible saturation curves. For example, if a particularadvertising campaign is assumed to have an effective frequency of 2 anda penetration of 70%, a range of plausible saturation curves may bedefined by plausible effective frequencies ranging from 1-4 andplausible penetrations ranging from 55%-85%. With a saturation equationdefined for any combination of the specified ranges of effectivefrequency and penetration (e.g., based on earlier simulations), it is arelatively straightforward task to determine which resulting curve fromthe range of plausible saturation curves best models the actual data. Todo so, a regression is run on the marketing mix model with respect tothe advertising campaign being analyzed for each of the plausiblesaturation curves to be tested. That is, a default saturation curve isfixed for every other advertising campaign in the marketing mix model(e.g., based on the initial estimate for effective frequency andpenetration for each campaign) and only the saturation curve for theadvertising campaign being analyzed is varied. Based on such aregression analysis, the saturation curve that produces a model thatbest fits the actual marketing mix model input data is identified as thebest fitting saturation curve. In some examples, by repeating thisprocess for each advertising campaign, a best fit saturation curve canbe determined for each advertising campaign. Then, the best fittingsaturation curve for each campaign can be used to transform theAdstocked GRPs for each corresponding campaign to ERR. Based on theresulting ERR for each campaign, a full regression can be run togenerate a final marketing mix model that incorporates the diminishingreturns effect of saturation. In this manner, more accurate predictionsof future sales can be made and enhancing (e.g., optimizing) futuremarketing endeavors can be made with greater confidence and reliabilitythan with currently known marketing mix systems.

FIGS. 8-11 illustrate graphs 800, 900, 1000, 1100 with the same raw GRPs102 and Adstocked GRPs represented by line 124 in graph 100 of FIG. 1 .The graphs 800, 900, 1000, 1100 also include a line 802, 902, 1002, 1102corresponding to the ERR from the Adstocked GRPs using Equation 2 withdifferent effective frequencies and penetrations. Specifically, the ERRrepresented by line 802 of the example graph 800 is associated with thesaturation curve 302 of FIG. 3 corresponding to an effective frequencyof 1 and a penetration of 20%. The ERR represented by line 902 of theexample graph 900 is associated with the saturation curve 402 of FIG. 4corresponding to an effective frequency of 1 and a penetration of 95%.The ERR represented by line 1002 of the example graph 1000 is associatedwith the saturation curve 304 of FIG. 3 corresponding to an effectivefrequency of 4 and a penetration of 20%. The ERR represented by line1102 of the example graph 1100 is associated with the saturation curve404 of FIG. 4 corresponding to an effective frequency of 4 and apenetration of 95%. The ERR is plotted with reference to the scale onthe right-hand axis corresponding to reach as a percentage. For purposesof comparison, the scale of the axes in each of the graphs 800, 1000,1100 go from 0% to 50% (the scale in the graph 900 goes from 0% to 100%because of the much higher ERR achieved during the diagramed timeperiod).

From FIGS. 8-11 it is apparent how much impact a change in thesaturation curve can have on the ERR calculated from the same AdstockedGRPs for an advertising campaign at any particular point during thecampaign. For example, although the Adstocked GRPs are identical in eachgraph 800, 900, 1000, 1100 (being based on the same raw GRPs), theresulting ERR calculated based on different saturation curves aresignificantly different. For instance, the lines 802, 902 of graphs 800,900 are both based on an effective frequency of 1 but line 802corresponds to a penetration of 20% whereas line 902 corresponds to apenetration of 95%. Based on this single difference, the ERR in graph800 hovers between approximately 18% and 20% (near the saturation point)from the third week 108 to the eighth week 118. In contrast, the ERR ingraph 900 reaches a peak of approximately 80% during the fourth week110, declines by half to an ERR of 40% by the seventh week 116, butbounces back to over 50% in the eighth week 118. Accordingly, higherpenetration values for an advertising campaign result in much greatervariation in the ERR from week to week depending upon whether additionalGRPs are purchased. In other words, a lower penetration results in aconsistent ERR being stretched out over time. Similar observations canbe made when comparing lines 1002, 1102 of graphs 1000, 1100 where theeffective frequency is fixed at 4 while line 1002 is associated with apenetration of 20% and line 1102 is associated with a penetration of95%. However, the high effective frequency, in combination with the highpenetration, results in a relatively low ERR without significant andconsistent GRPs being delivered.

Furthermore, a comparison of line 802 of graph 800 with line 1002 ofgraph 1000 demonstrates the impact of different effective frequencies(e.g., 1 for line 802 and 4 for line 1002) for a fixed penetration(e.g., 20%). In particular, the higher the effective frequency, the moreabruptly the ERR rises or falls depending upon the amount of GRPsdelivered. For example, although the ERR in graph 800 rises quicklyinitially (which is characteristic for an effective frequency of 1), therising and falling of the ERR thereafter is relatively gradual (e.g.,from the eighth week 118 to the tenth week 122 the ERR in graph 800declines by a little more than a third). In contrast, in graph 1000where the effective frequency is 4, the ERR rises and falls much moreabruptly (e.g., from the eighth week 118 to the tenth week 122 the ERRin graph 1000 is nearly entirely dissipated). Again, the same phenomenonis demonstrated by the lines 902, 1102 of graphs 900, 1100 where thepenetration is fixed at 95%.

Thus, the diminishing returns effect of saturation as determined fromthe effective frequency and penetration associated with a particularadvertising campaign can significantly affect the variation of the ERRobserved over time as well as how abruptly that variation occurs.Further, such knowledge can significantly improve marketing mix modelsto more accurately represent historical data and, therefore, can moreaccurately predict the impact of particular marketing schemes on futuresales and/or more reliably plan new marketing campaigns. However, noneof this information is available with currently known marketing mixsystems because the model estimation does not take saturation intoaccount. While a market analyst may try to account for saturation afterthe fact, any such efforts are limited in that they are not based on, orfit to, actual data.

FIG. 12 illustrates graph 1200 with the same plotted data points asshown in the graph 200 of FIG. 2 . However, unlike the graph 200 of FIG.2 , the graph 1200 of FIG. 12 includes a best fitting response curve1202 calculated using some of the teachings disclosed herein. Asdescribed above in connection with FIG. 2 , the data points plotted inthe graph 1200 are based outputs of a known marketing mix model (i.e.,does not account for saturation during model estimation). As shown inthe illustrated example, unlike the response curve 202 (which is astraight line) the best fitting response curve 1202 follows a curveindicative of a diminishing returns effect. While market analysts mayadjust the response curve 202 after model estimation to imitatesaturation, the response curve 1202 of the illustrated example isdetermined based on modified saturation curves 1204 that are calculatedsimilar to the saturation curves calculated above (e.g., based onplausible ranges of effective frequencies and penetrations associatedwith the advertising campaign being analyzed) and then scaled torepresent lift rather than reach. More particularly, in some examples, aplausible range of modified saturation curves are calculated and thentested for best fit against the model output data. The two best fittingcurves that bound the data (e.g., the modified saturation curves 1204)are identified and set as boundaries for determining the best fitresponse curve 1202. In this manner, even without incorporatingsaturation into model estimation, the resulting best fit response curve1202 is still an improvement over the response curve 202 and does notrequire guesswork by an analyst to correct it for saturation after thefact.

Although the example response curve 1202 described in connection withFIG. 12 provides an improvement over known marketing mix systems, evenmore reliable response curves can be obtained when saturation isincorporated into model estimation as has been described above. FIG. 13illustrates an example graph 1300 with a response curve 1302 fit to datapoints 1304 associated with lift for a particular advertising campaignoutput from a known marketing mix model (e.g., without saturation).Additionally, the example graph 1300 of FIG. 13 includes anotherresponse curve 1306 fit to data points 1308 associated with lift for thesame advertising campaign output from a marketing mix model generated inaccordance with the teachings disclosed herein (e.g., with saturation).As discussed above in connection with FIG. 2 , the response curve 1302that best fits the data points 1304 is a straight line and, therefore,unreliable for evaluating marketing endeavors going forward. Incontrast, the response curve 1306 follows a curve that would be expectedbased on the diminishing returns effect of increased GRPs. Furthermore,the response curve 1306 closely fits the data points 1308 output by themarketing mix model. Accordingly, the response curve 1306 is not basedon the intuition of market analysts trying to correct the straight lineof the curve 1302 after the fact, but is based on actual data. As such,the response curve 1306 is far more reliable in evaluating futureadvertising campaigns to forecast future sales and/or to plan and/oradjust a marketing mix scheme to enhance (e.g., maximize) a return oninvestment.

FIG. 14 is a schematic illustration of an example marketing mix modelgenerator 1400 constructed in accordance with the teachings disclosedherein. In the illustrated example of FIG. 14 , the example marketingmix model generator 1400 includes an adstock calculator 1402, apenetration range determiner 1404, an effective frequency rangedeterminer 1406, a saturation curve calculator 1408, a marketingsimulator 1410, a regression engine 1412, an ERR calculator 1414, anaudience measurement database 1416, a saturation curve database 1418,and a marketing mix inputs database 1420.

In operation, the marketing mix inputs database 1420 stores informationused as inputs to be analyzed in generating a marketing mix model. Insome examples, inputs for the model estimation include the time-phasedexpenditure for various media (e.g., television, radio, print, online,etc.) in different geographical locations (e.g., measured in GRPs), theamount of trade or promotional spending (e.g., measured in GRPs),seasonal factors (e.g., weather), sales data for one or more products orservices over time, and any other information that may be deemed to beimportant in determining sales (e.g., macro-economic factors). Theexample marketing mix model generator 1400 is provided with the adstockcalculator 1402 to convert the raw GRPs associated with each advertisingcampaign into effective GRPs realized over time (i.e., Adstocked GRPs).

The example marketing mix model generator 1400 is provided with thepenetration range determiner 1404 and the effective frequency rangedeterminer 1406 to determine a range of plausible penetrations andeffective frequencies to define corresponding plausible saturationcurves to be tested for best fit to the model data. In some examples, apenetration range is determined based on demographic data and media typeinformation stored in the audience measurement database 1416. Inparticular, in some such examples, the penetration range determiner 1404identifies an initial penetration based on the demographics of thetarget audience for each advertising campaign compared with the storeddemographic data associated with the media type corresponding to eachadvertising campaign. Once the initial penetration estimate isdetermined, in some examples, a reasonable range of penetration valuessurrounding the initial penetration are selecting for testing (e.g., 15%above and below the initial penetration estimate). Additionally oralternatively, in some examples, other attributes associated with theadvertising campaign are used to infer an initial penetration estimateincluding the geographic region of the advertising campaign, thepenetration of comparable campaigns associated with related and/orcompeting products, and/or the results of previous marketing mixstudies. In other examples, where specific data to infer penetration(e.g., demographic data, other comparable campaigns, etc.) is notavailable or otherwise unreliable, the penetration range determiner 1404selects a broad range of penetration values based on the media type ofthe advertising campaign being analyzed. In some examples, a marketanalyst may broaden, narrow, or otherwise adjust the identified range ofpenetrations to be tested based on their confidence of theappropriateness of the initial penetration and/or knowledge of theparticular advertising campaign being analyzed. Additionally, theanalyst may define a granularity of penetration values to be tested overthe identified range (e.g., every 3%, 1%, 0.5% etc.).

The effective frequency range determiner 1406 determines a range ofplausible effective frequencies to be tested based on the nature andcomplexity of the particular advertising campaign and/or other relevantconsiderations (e.g., the known effective frequency of comparablecampaign advertisements for related and/or competing products, etc.). Insome examples, the range of effective frequencies is based on an initialeffective frequency estimate input by a market analyst. In someexamples, the effective frequency range determiner 1406 defines a lowerlimit for the effective frequency range to be 1 regardless of the natureof the advertising campaign. Further, in some examples, the analyst maybroaden, narrow, or otherwise adjust the identified range of effectivefrequencies and/or the granularity of the effective frequencies to betested within the range.

The example marketing mix model generator 1400 is provided with thesaturation curve calculator 1408 to calculate the curves in the range ofplausible saturation curves defined by the identified ranges ofpenetrations and effective frequencies. In some examples, the saturationcurve calculator 1408 retrieves or looks up the saturation curve in thesaturation curve database 1418. In such examples, the saturation curvedatabase 1418 stores a predetermined saturation equation definingsaturation curves for any expected penetration value in combination withany expected effective frequency. In some examples, where a curvecorresponding to a particular penetration and/or effective frequency isnot available for look up in the saturation curve database 1418 (or thesaturation curve database 1418 is unavailable), the saturation curvecalculator 1408 calculates the saturation curve through a simulation viathe marketing simulator 1410. In such examples, the marketing simulator1410 simulates an advertising campaign at the specified penetrationvalue by plotting simulated GRPs against a resulting reach of a seriesof advertising messages. Based on the plot of the GRPs associated with areach at the specified effective frequency a curve can be defined thatfits the simulated data. In some examples, the curves used to match thesimulated data and/or the curves stored in the saturation curve database1418 are defined by Weibull functions. However, any other equations thatfit the data may alternatively be used. In some examples, the saturationcurve calculator 1408 calculates (or looks up) a saturation curve forevery possible pairing of the effective frequencies identified withinthe range of plausible effective frequencies and the penetrationsidentified within the range of plausible penetrations. In this manner, arange of plausible saturation curves are calculated to be tested for abest fit to the model data. In other examples, the range of plausiblesaturation curves is based on only some of the effective frequenciespaired with only some of the penetrations within the correspondingranges to improve computational efficiency.

The example marketing mix model generator 1400 is provided with theregression engine 1412 to determine the saturation curve among the rangeof plausible saturation curves that best fits the model data stored inthe marketing mix inputs database 1420. In some examples, a regressionis run on all the model data with the saturation curves used for eachadvertising campaign being held constant except for the saturation curveassociated with the advertising campaign being analyzed for best fit.That is, while each advertising campaign will have a separate range ofsaturation curves to be tested for best fit, when determining the bestfit curve of a particular advertising campaign each curve in the rangeof plausible saturation curves corresponding to the particular campaignis run through the regression engine while a default saturation curve isset for each of the other advertising campaigns during all of thesaturation curves tested for the particular campaign being analyzed. Insome examples, the default saturation curve for each advertisingcampaign corresponds to the saturation curve defined by the initialestimate of the penetration and effective frequency associated with thecorresponding advertising campaign. In other examples, the defaultsaturation curve is set as the curve defined by the midpoint penetrationof the range of plausible penetrations and the midpoint effectivefrequency of the range of plausible effective frequencies for eachcampaign. In other examples, other methods of setting the defaultsaturation curve may alternatively be implemented. In some examples, thecurves within the range of plausible saturation curves are calculated(looked up) by the saturation curve calculator 1408 in conjunction withthe regression performed via the regression engine 1412. That is, insuch examples, a first saturation curve within the range of plausiblesaturation curves is calculated and then the regression engine 1412generates a marketing mix model based on the calculated curve anddefault saturation curves for all other advertising campaigns. Then, asecond saturation curve (e.g., having a different penetration and/oreffective frequency than the first saturation curve) within the range ofplausible saturation curves is similarly calculated and subsequently runthrough the regression.

Furthermore, while the regression engine 1412 may run through each curvein the range of plausible saturation curves calculated by the saturationcurve calculator 1408, in other examples, the regression engine onlyruns through some of the curves In the range of plausible saturationcurves defined by the identified ranges of penetration and effectivefrequency. For instance, in some such examples, a default effectivefrequency (e.g., the midpoint within the range of plausible effectivefrequencies) is fixed while each penetration in the range of plausiblepenetrations is evaluated to calculate a series of saturation curves. Insuch examples, the series of saturation curves (all associated with thesame effective frequency) are analyzed by the regression engine 1412 todetermine a best fit penetration corresponding to the best fitsaturation curve in the series analyzed. In some such examples, theidentified best fit penetration is then set as a default penetration andanother series of saturation curves are calculated based on varying theeffective frequency over the entire range of plausible effectivefrequencies. In the same manner as above, in some examples, the secondseries of saturation curves (all associated with the same penetration)are analyzed by the regression engine 1412 to determine a best fiteffective frequency. Then, based on the best first penetration and bestfit effective frequency the saturation curve calculator 1408 calculates(or looks up) a corresponding saturation curve that is then designatedas the best fit saturation curve. In other examples, the best fiteffective frequency is determined first and then the best fitpenetration is determined.

The example marketing mix model generator 1400 is provided with the ERRcalculator 1414 to transform or convert the Adstocked GRPs calculated bythe adstock calculator 1402 into ERR for each advertising campaign. TheERR calculator 1414 transforms the Adstocked GRPs via the best fitsaturation curve identified by the saturation curve calculator 1408 andregression engine 1420 as described above. Once the Adstocked GRPs foreach advertising campaign to be analyzed have been transformed to ERRbased on the best fit saturation curve associated with each campaign,the regression engine 1412 then runs the ERR data for each campaignthrough a full regression to generate a final marketing mix modelestimation that can then be evaluated to forecast future sales and/ormake plans for future marketing endeavors that enhance (e.g., optimize)the use of budgeted marketing funds as is known in the art.

While an example manner of implementing the example marketing mix modelgenerator 1400 of FIG. 14 is illustrated in FIG. 14 , one or more of theelements, processes and/or devices illustrated in FIG. 14 may becombined, divided, re-arranged, omitted, eliminated and/or implementedin any other way. Further, the example adstock calculator 1402, theexample penetration range determiner 1404, the example effectivefrequency range determiner 1406, the example saturation curve calculator1408, the example marketing simulator 1410, the example regressionengine 1412, the example ERR calculator 1414, the example audiencemeasurement database 1416, the example saturation curve database 1418,the example marketing mix inputs database 1420 and/or, more generally,the example marketing mix model generator 1400 of FIG. 14 may beimplemented by hardware, software, firmware and/or any combination ofhardware, software and/or firmware. Thus, for example, any of theexample adstock calculator 1402, the example penetration rangedeterminer 1404, the example effective frequency range determiner 1406,the example saturation curve calculator 1408, the example marketingsimulator 1410, the example regression engine 1412, the example ERRcalculator 1414, the example audience measurement database 1416, theexample saturation curve database 1418, the example marketing mix inputsdatabase 1420 and/or, more generally, the example marketing mix modelgenerator 1400 could be implemented by one or more circuit(s),programmable processor(s), application specific integrated circuit(s)(ASIC(s)), programmable logic device(s) (PLD(s)) and/or fieldprogrammable logic device(s) (FPLD(s)), etc. When reading any of theapparatus or system claims of this patent to cover a purely softwareand/or firmware implementation, at least one of the example adstockcalculator 1402, the example penetration range determiner 1404, theexample effective frequency range determiner 1406, the examplesaturation curve calculator 1408, the example marketing simulator 1410,the example regression engine 1412, the example ERR calculator 1414, theexample audience measurement database 1416, the example saturation curvedatabase 1418, and/or the example marketing mix inputs database 1420 arehereby expressly defined to include a tangible computer readable storagedevice or storage disc such as a memory, DVD, CD, Blu-ray, etc. storingthe software and/or firmware. Further still, the example marketing mixmodel generator 1400 of FIG. 14 may include one or more elements,processes and/or devices in addition to, or instead of, thoseillustrated in FIG. 14 , and/or may include more than one of any or allof the illustrated elements, processes and devices.

Flowcharts representative of example machine readable instructions forimplementing the example marketing mix model generator 1400 of FIG. 14are shown in FIGS. 15-17 . In these examples, the machine readableinstructions comprise a program for execution by a processor such as theprocessor 1812 shown in the example processor platform 1800 discussedbelow in connection with FIG. 18 . The program may be embodied insoftware stored on a tangible computer readable storage medium such as aCD-ROM, a floppy disk, a hard drive, a digital versatile disk (DVD), aBlu-ray disk, or a memory associated with the processor 1812, but theentire program and/or parts thereof could alternatively be executed by adevice other than the processor 1812 and/or embodied in firmware ordedicated hardware. Further, although the example program is describedwith reference to the flowcharts illustrated in FIGS. 15-17 , many othermethods of implementing the example marketing mix model generator 1400may alternatively be used. For example, the order of execution of theblocks may be changed, and/or some of the blocks described may bechanged, eliminated, or combined.

As mentioned above, the example processes of FIGS. 15-17 may beimplemented using coded instructions (e.g., computer and/or machinereadable instructions) stored on a tangible computer readable storagemedium such as a hard disk drive, a flash memory, a read-only memory(ROM), a compact disk (CD), a digital versatile disk (DVD), a cache, arandom-access memory (RAM) and/or any other storage device or storagedisk in which information is stored for any duration (e.g., for extendedtime periods, permanently, for brief instances, for temporarilybuffering, and/or for caching of the information). As used herein, theterm tangible computer readable storage medium is expressly defined toinclude any type of computer readable storage device and/or storage diskand to exclude propagating signals. As used herein, “tangible computerreadable storage medium” and “tangible machine readable storage medium”are used interchangeably. Additionally or alternatively, the exampleprocesses of FIGS. 15-17 may be implemented using coded instructions(e.g., computer and/or machine readable instructions) stored on anon-transitory computer and/or machine readable medium such as a harddisk drive, a flash memory, a read-only memory, a compact disk, adigital versatile disk, a cache, a random-access memory and/or any otherstorage device or storage disk in which information is stored for anyduration (e.g., for extended time periods, permanently, for briefinstances, for temporarily buffering, and/or for caching of theinformation). As used herein, the term non-transitory computer readablemedium is expressly defined to include any type of computer readabledevice or disc and to exclude propagating signals. As used herein, whenthe phrase “at least” is used as the transition term in a preamble of aclaim, it is open-ended in the same manner as the term “comprising” isopen ended.

The example program of FIG. 15 begins at block 1500 where the exampleadstock calculator 1402 converts raw GRPs of an advertising campaigninto Adstocked GRPs. In some examples, the example adstock calculator1402 converts raw GRPs via Equation 1. Such a transformation of raw GRPsis known in the art and not further described here. At block 1500, theexample adstock calculator 1402 determines whether there is anotheradvertising campaign with raw GRPs to be converted to Adstocked GRPs. Ifthe example adstock calculator 1402 determines that there is anotheradvertising campaign to be analyzed, control returns to block 1500.

If the example adstock calculator 1402 determines there are noadditional advertising campaigns to be analyzed to calculate AdstockedGRPs (block 1502), control advances to block 1504 where the examplesaturation curve calculator 1408 calculates plausible saturation curvesfor an advertising campaign. As described above, in some examples, theexample saturation curve calculator 1408 calculates a range of plausiblesaturation curves based on ranges of plausible effective frequencies andpenetrations determined via the example penetration range determiner1404 and example effective frequency determiner 1406. In some examples,the example saturation curve calculator 1408 retrieves the plausiblesaturation curves from the saturation curve database 1418 by lookingthem up based on the ranges of plausible effective frequencies andpenetrations. In other examples, where saturation curves are notavailable for look up, the example saturation curve calculator 1408invokes the example marketing simulator 1410 to generate simulated datapoints of GRPs that can be plotted against reach to determine acorresponding saturation curve. Additional details associated withcalculating plausible saturation curves and simulating an advertisingcampaign are described below in connection with the example processes ofFIGS. 16 and 17 . At block 1506, the example saturation curve calculator1408 determines whether there is another advertising campaign for whichplausible saturation curves are to be calculated. If the examplesaturation curve calculator 1408 determines that there is anotheradvertising campaign for which plausible saturation curves are to becalculated, control returns to block 1504.

If the example saturation curve calculator 1408 determines there are noadditional advertising campaigns for which plausible saturation curvesare to be calculated (block 1506), control advances to block 1508 wherethe example regression engine 1412 determines the saturation curve forthe advertising campaign that best fits the marketing mix input data. Asdescribed above, in some examples, the example regression engine 1412runs some or all of the saturation curves calculated by the examplesaturation curve calculator 1408 (block 1504) through a regression toidentify the saturation curve among the plausible saturation curves thatbest fits the marketing mix input data stored in the example marketingmix inputs database 1420.

At block 1510, the example saturation curve database 1418 stores thebest fitting saturation curve for the advertising campaign. In thismanner, when a similar advertising campaign is to be analyzed, in thesame or a different marketing mix model, the stored saturation curve canbe retrieved as an initial estimate of the saturation curve for thesimilar advertising campaign to provide more refined results and/or anarrow range of plausible saturation curves to increase computationalefficiency.

At block 1512, the example ERR calculator 1414 converts the AdstockedGRPs for an advertising campaign into ERR for the campaign. In someexamples, the example ERR calculator 1414 transforms the Adstocked GRPsinto ERR based on a saturation equation that defines the best fittingsaturation curve determined by the example regression engine 1412 (block1508). In some examples, the saturation equation corresponds to aWeibull function. At block 1514, the example regression engine 1412determines whether there is another advertising campaign for which abest fitting saturation curve is to be determined. If the exampleregression engine 1412 determines there is another such advertisingcampaign, controls returns to block 1508.

If the example regression engine 1412 determines there are no otheradvertising campaign for which a best fitting saturation curve is to bedetermined, control advances to block 1516 where the example regressionengine 1412 generates a marketing mix model. In some examples, thegenerated marketing mix model is based on a regression analysis of thebest fitting saturation curve for each advertising campaign relative tothe information stored in the example marketing mix inputs database1420. In this manner, the contribution of each advertising campaignimpacting sales may be determined while accounting for the diminishingreturns effect of saturation and subsequently evaluated using methodsknown in the art. Accordingly, once the example regression engine 1412has generated the marketing mix model, the example process of FIG. 15ends.

FIG. 16 illustrates an example process with additional detail forimplementing block 1504 of the example process of FIG. 15 to calculateplausible saturation curves for an advertising campaign. The exampleprocess of FIG. 16 begins at block 1600 where the example penetrationrange determiner 1404 determines a range of penetrations to be analyzed.In some examples, the example penetration range determiner 1404determines the range of penetrations by identifying an initialpenetration estimate. In some examples, the initial penetration estimateis based on the media type and/or demographic information stored in theaudience measurement database. In other examples, the initialpenetration is based on the penetration associated with a saturationcurve stored in the example saturation curve database 1418 thatcorresponds to an advertising campaign similar to the advertisingcampaign being analyzed. Additionally or alternatively, the examplepenetration range determiner 1404 may consider other factors todetermine the range of penetrations associated with the advertisingcampaign (e.g., geographic region, penetrations for related or competingproducts, etc.) With the initial penetration estimate identified, theexample penetration range determiner 1404 determines a range ofplausible penetrations surrounding the initial penetration estimate foranalysis.

At block 1602, the example effective frequency range determiner 1404determines a range of effective frequencies to be analyzed. In someexamples, the example effective frequency range determiner 1404determines the range of effective frequencies by identifying a range ofeffective frequencies surrounding an initial effective frequency inputby a marketing analyst (e.g., based on a complexity of theadvertisement). In some examples, the initial effective frequency isbased on the effective frequency associated with a saturation curvestored in the example saturation curve database 1418 that corresponds toan advertising campaign similar to the advertising campaign beinganalyzed.

At block 1604, the example saturation curve calculator 1408 identifies afirst penetration from the range of penetrations and a first effectivefrequency from the range of effective frequencies. In some examples, thefirst penetration and first effective frequency correspond to theinitial penetration and initial effective frequency. In other examples,the first penetration and first effective frequency correspond to apenetration and effective frequency at a lower or upper end of thecorresponding range of penetrations and range of effective frequencies.In some examples, the first penetration and first effective frequencycorrespond to midpoints within the corresponding range of penetrationsand range of effective frequencies.

At block 1606, the example saturation curve calculator 1408 determineswhether the identified penetration and effective frequency correspond toa saturation curve stored in the saturation curve database 1418. If acorresponding saturation curve is stored in the saturation curvedatabase 1418, the example saturation curve calculator 1408 retrievesthe corresponding saturation curve at block 1608. After the saturationcurve is retrieved, control advances to block 1614 where the examplesaturation curve calculator 1408 determines whether to calculate anothersaturation curve as will be described more fully below. If the examplesaturation curve calculator 1408 determines that the identifiedpenetration and effective frequency do not correspond to a saturationcurve stored in the saturation curve database 1418, control advances toblock 1610.

At block 1610, the example saturation curve calculator 1408 calculates asaturation curve corresponding to the identified penetration andeffective frequency based on a simulated advertising campaign.Additional details associated with simulating an advertising campaignare described below in connection with the example process of FIG. 17 .At block 1612, the example saturation curve calculator 1408 stores thecalculated saturation curve in the saturation curve database 1418. Inthis manner, if the same penetration and effective frequency areidentified while analyzing another advertising campaign, thecorresponding saturation curve can be retrieved from the database (block1608) rather than simulating another advertising campaign (block 1610).

At block 1614 the example saturation curve calculator 1408 determineswhether another saturation curve is to be calculated. In some examples,the saturation curve calculator 1408 will calculate saturation curvesfor all pairings of penetrations and effective frequencies in thecorresponding range of penetrations and range of effective frequencies.In other examples, only some of the penetrations and/or effectivefrequencies will be used to calculate saturation curves. For instance,in some examples, a single default effective frequency will be usedwhile the example saturation curve calculator 1408 calculates asaturation curve corresponding to each penetration within the range ofpenetrations. In some such examples, the resulting saturation curveswill be analyzed via the example regression engine 1412 (similar toblock 1508 of FIG. 15 ) to determine a best fit penetration before adefault penetration (e.g., the best fit penetration) is used while theexample saturation curve calculator 1408 calculates a saturation curvecorresponding to each effective frequency within the range of effectivefrequencies. Accordingly, if the example saturated curve calculator 1408determines another saturation curve is to be calculated (block 1608),control advances to block 1616 where the example saturation curvecalculator 1408 modifies at least one of the penetration or effectivefrequency associated with the previous saturation curve(s) calculated.For example, as described above, the effective frequency (or thepenetration) may be held constant while different penetrations (oreffective frequencies) are used to calculate different saturationcurves. However, other methods of modifying the effective frequency andpenetration to be used in calculating the saturation curves mayalternatively be implemented.

Once at least one of the penetration or the effective frequencyassociated with previous saturation curve(s) have been modified (block1616), control returns to block 1606 where the corresponding curve maybe either retrieved (block 1608) or calculated based on a simulatedadvertising campaign (block 1610) as described above. Returning to block1614, if the example saturated curve calculator 1408 determines that noother saturation curves are to be calculated, the example process ofFIG. 16 ends.

FIG. 17 illustrates an example process with additional detail forimplementing block 1604 and/or block 1610 of the example process of FIG.16 to calculate plausible saturation curves for an advertising campaignby simulating an advertising campaign. The example process of FIG. 17begins at block 1700 where the example marketing simulator 1410 definesa simulated target population (e.g., 10,000 individuals (orhouseholds)). At block 1702 the example marketing simulator 1410 selectsa subset of members in the target population based on the identifiedpenetration. For example, if the penetration determined by the examplepenetration range determiner 1404 is 60%, the example marketingsimulator 1410 would select 60% of the target population asrepresentative of individuals (or households) capable of being reachedby the advertising campaign (e.g., 6,000 of the 10,000 totalpopulation).

At block 1704, the example marketing simulator 1410 randomly selects aportion of the subset of members for exposure to a simulatedadvertisement. The portion of members selected by the example marketingsimulator 1410 is based on the simulated GRPs associated with thesimulated advertisement. For example, if the simulated advertisement isassociated with 5 GRPs, the corresponding reach of the advertisementwould be 5% of the target population (e.g., 500 members randomlyselected from the 6,000 members identified based on the penetration). Atblock 1706, the example marketing simulator 1410 records the number oftimes each member of the target population is exposed to theadvertisement. After the first advertisement, the number of time the 500members are exposed to the advertisement would be one, while the numberof times all other members in the population are exposed to theadvertisement would zero. However, as is described more fully below inconnection with block 1712, the example process of FIG. 17 may iteratethrough multiple simulated advertisements. In such examples, some of theinitial 500 members may be randomly selected for exposure to thesimulated advertisement a second time, while the advertisement would bethe first exposure for other randomly selected members. Accordingly, theexample marketing simulator 1410 records the number of times each memberof the target population is exposed to the advertisement, which may varyfrom member to member as more advertisements are simulated.

At block 1708 the example marketing simulator 1410 totals the GRPsdelivered corresponding to all simulated advertisements. That is, afterthe first simulated advertisement, the total GRPs corresponds to theGRPs associated with the first advertisement. However, after multiplesimulated advertisements, the total GRPs corresponds to the sum of theGRPs associated with each of the simulated advertisements. At block 1710the example marketing simulator 1410 plots the total reach achieved atthe identified effective frequency against the total GRPs delivered. Theidentified effective frequency is based on the effective frequencyidentified by the effective frequency range determiner 1406 and thetotal reach achieved corresponds to the number of members having beenexposed to the simulated advertisements at least the same amount as theeffective frequency. For example, if the effective frequency is 2, thereach would correspond to the number of members that were exposed to thesimulated advertisements at least 2 times. In some examples, the examplemarketing simulator 1410 calculates the reach as a percentage bydividing the total number reached by the total size of the targetpopulation.

At block 1712, the example marketing simulator 1410 determines whetherto simulate another advertisement. In some examples, the examplemarketing simulator 1410, advertisements continue to be simulated untilthe total reach plotted levels off near the penetration. That is, theexample marketing simulator 1410 continue simulating advertisementsuntil all or nearly all of the subset of members have been exposed tothe advertisement at least as many times as the effective frequency. Ifthe example marketing simulator 1410 determines to simulate anotheradvertisement, control returns to block 1704. If the example marketingsimulator 1410 determines to not to simulate another advertisement,control advances to block 1714 where the example saturation curvecalculator 1408 calculates a curve that matches the plotted reachagainst GRPs. The resulting curve corresponds to the saturation curvedefined by the penetration and effective frequency used in the exampleprocess of FIG. 16 . Thus, once the example saturation curve calculator1408 calculates a curve that matches the plotted reach against GRPs, theexample process of FIG. 17 ends.

FIG. 18 is a block diagram of an example processor platform 1800 capableof executing the instructions of FIGS. 15-17 to implement the examplemarketing mix model generator 1400 of FIG. 14 . The processor platform1800 can be, for example, a server, a personal computer, a mobile device(e.g., a cell phone, a smart phone, a tablet such as an iPad™), apersonal digital assistant (PDA), an Internet appliance, or any othertype of computing device.

The processor platform 1800 of the illustrated example includes aprocessor 1812. The processor 1812 of the illustrated example ishardware. For example, the processor 1812 can be implemented by one ormore integrated circuits, logic circuits, microprocessors or controllersfrom any desired family or manufacturer.

The processor 1812 of the illustrated example includes a local memory1813 (e.g., a cache). The processor 1812 of the illustrated example isin communication with a main memory including a volatile memory 1814 anda non-volatile memory 1816 via a bus 1818. The volatile memory 1814 maybe implemented by Synchronous Dynamic Random Access Memory (SDRAM),Dynamic Random Access Memory (DRAM), RAMBUS Dynamic Random Access Memory(RDRAM) and/or any other type of random access memory device. Thenon-volatile memory 1816 may be implemented by flash memory and/or anyother desired type of memory device. Access to the main memory 1814,1816 is controlled by a memory controller.

The processor platform 1800 of the illustrated example also includes aninterface circuit 1820. The interface circuit 1820 may be implemented byany type of interface standard, such as an Ethernet interface, auniversal serial bus (USB), and/or a PCI express interface.

In the illustrated example, one or more input devices 1822 are connectedto the interface circuit 1820. The input device(s) 1822 permit a user toenter data and commands into the processor 1812. The input device(s) canbe implemented by, for example, an audio sensor, a microphone, a camera(still or video), a keyboard, a button, a mouse, a touchscreen, atrack-pad, a trackball, isopoint and/or a voice recognition system.

One or more output devices 1824 are also connected to the interfacecircuit 1820 of the illustrated example. The output devices 1824 can beimplemented, for example, by display devices (e.g., a light emittingdiode (LED), an organic light emitting diode (OLED), a liquid crystaldisplay, a cathode ray tube display (CRT), a touchscreen, a tactileoutput device, a light emitting diode (LED), a printer and/or speakers).The interface circuit 1820 of the illustrated example, thus, typicallyincludes a graphics driver card.

The interface circuit 1820 of the illustrated example also includes acommunication device such as a transmitter, a receiver, a transceiver, amodem and/or network interface card to facilitate exchange of data withexternal machines (e.g., computing devices of any kind) via a network1826 (e.g., an Ethernet connection, a digital subscriber line (DSL), atelephone line, coaxial cable, a cellular telephone system, etc.).

The processor platform 1800 of the illustrated example also includes oneor more mass storage devices 1828 for storing software and/or data.Examples of such mass storage devices 1828 include floppy disk drives,hard drive disks, compact disk drives, Blu-ray disk drives, RAIDsystems, and digital versatile disk (DVD) drives.

The coded instructions 1832 of FIGS. 15-10 may be stored in the massstorage device 1828, in the volatile memory 1814, in the non-volatilememory 1816, and/or on a removable tangible computer readable storagemedium such as a CD or DVD.

Although certain example methods, apparatus and articles of manufacturehave been described herein, the scope of coverage of this patent is notlimited thereto. On the contrary, this patent covers all methods,apparatus and articles of manufacture fairly falling within the scope ofthe claims of this patent.

What is claimed is:
 1. An apparatus comprising: memory; machine-readableinstructions; and processor circuitry to execute the machine-readableinstructions to: identify a number of times respective members of atarget population are exposed to an advertisement associated with asimulated advertising campaign; determine a total of gross rating pointsdelivered in the simulated advertising campaign, the total of grossrating points delivered corresponding to a sum of first gross ratingpoints associated with a first simulation of the advertisement andsecond gross rating points associated with a second simulation of theadvertisement; determine a total reach achieved relative to the total ofgross rating points delivered; calculate a saturation curve based on thetotal reach relative to the total of gross rating points delivered; andstore the saturation curve as one of a plurality of plausible curves forincorporation of saturation effects into a marketing mix model, theplurality of plausible curves to eliminate adjustment of a responsecurve associated with a second advertising campaign after generation ofthe marketing mix model, the second advertising campaign different thanthe simulated advertising campaign.
 2. The apparatus of claim 1, whereinthe respective members define a subset of members of the targetpopulation, the processor circuitry to define the subset based on anidentified penetration for the second advertising campaign.
 3. Theapparatus of claim 2, wherein the processor circuitry is to randomlyselect the subset to be exposed to the advertisement.
 4. The apparatusof claim 1, wherein the total reach achieved corresponds to a number ofthe members exposed to the advertisement at least a same amount as aneffective frequency for the second advertising campaign.
 5. Theapparatus of claim 4, wherein the processor circuitry is to causesimulations of the advertisement to be repeated until respective ones ofthe members have been exposed to the advertisement at least the sameamount as the effective frequency.
 6. The apparatus of claim 4, whereinthe effective frequency corresponds to an initial effective frequencyidentified for the second advertising campaign.
 7. The apparatus ofclaim 4, wherein the effective frequency is within a range of effectivefrequencies identified for the second advertising campaign.
 8. Theapparatus of claim 4, wherein the saturation curve is a first saturationcurve, and the processor circuitry is to identify the effectivefrequency based on a second saturation curve associated with a thirdadvertising campaign, the third advertising campaign different than thesimulated advertising campaign and the second advertising campaign. 9.The apparatus of claim 1, wherein the processor circuitry is to:determine a penetration for the second advertising campaign; define asubset of the target population based on the penetration, the subsetincluding the respective members; and randomly select a portion of thesubset to be exposed to the advertisement.
 10. The apparatus of claim 9,wherein the saturation curve is a first saturation curve, and theprocessor circuitry is to: modify the penetration for the secondadvertising campaign; and determine a second saturation curve for thesecond advertising campaign based on exposure of the respective membersof the target population to the advertisement and the modifiedpenetration.
 11. A non-transitory machine readable storage mediumcomprising instructions to cause processor circuitry to at least:identify a number of times respective members of a target population areexposed to an advertisement associated with a simulated advertisingcampaign; determine a total of gross rating points delivered in thesimulated advertising campaign, the total of gross rating pointsdelivered corresponding to a sum of first gross rating points associatedwith a first simulation of the advertisement and second gross ratingpoints associated with a second simulation of the advertisement;determine a total reach achieved relative to the total of gross ratingpoints delivered; calculate a saturation curve based on the total reachrelative to the total of gross rating points delivered; and store thesaturation curve as one of a plurality of plausible curves forincorporation of saturation effects into a marketing mix model, theplurality of plausible curves to eliminate adjustment of a responsecurve associated with a second advertising campaign after generation ofthe marketing mix model, the second advertising campaign different thanthe simulated advertising campaign.
 12. The non-transitory machinereadable storage medium of claim 11, wherein the respective membersdefine a subset of members of the target population, the subsetidentified based on an identified penetration for the second advertisingcampaign.
 13. The non-transitory machine readable storage medium ofclaim 12, wherein the processor circuitry is to randomly select thesubset to be exposed to the advertisement.
 14. The non-transitorymachine readable storage medium of claim 11, wherein the total reachachieved corresponds to a number of the members exposed to theadvertisement at least a same amount as an effective frequency for thesecond advertising campaign.
 15. The non-transitory machine readablestorage medium of claim 14, wherein the processor circuitry is to causethe advertisement to be repeated until respective ones of the membershave been exposed to the advertisement at least the same amount as theeffective frequency.
 16. The non-transitory machine readable storagemedium of claim 14, wherein the effective frequency corresponds to aninitial effective frequency identified for the second advertisingcampaign.
 17. The non-transitory machine readable storage medium ofclaim 14, wherein the effective frequency is within a range of effectivefrequencies identified for the second advertising campaign.